Math REU at Kent State University
Mailing addressREU program
Dept. of Math Sciences
Kent State University
Math & CS Building
Summit Street, Kent OH 44242
reu [at] math.kent.edu
FAX: (330) 672-2209
Interactions between Linear Algebra and Ring Theory (Misha Chebotar)
We will study some problems that attract attention of researchers working in Linear Algebra and Ring Theory. The recently completed projects of my REU groups On maps preserving zeros of Lie polynomials of small degrees and On multilinear polynomials in four variables evaluated on matrices can serve as samples of such problems. See also paper #16 in Top 25 Hottest Articles list.
Prerequisites: Advanced Linear Algebra or Theory of Matrices, Ring Theory or Modern Algebra.
Publication produced: Benjamin E. Anzis, Zachary Emrich, Kaavya Valiveti On the images of Lie polynomials evaluated on Lie algebras, Linear Algebra and its Applications 469, 15, March 2015, Pages 51-75.
In elementary and analytic number theory, it is fundamental to study the asymptotic distributions of various arithmetic functions. In particular, some more important arithmetic functions, such as the divisor function, Euler's totient function, the sum-of-divisors function, etc, have received a lot of attention and been studied for many years. The objective of this project is to study the distribution of some hybrid arithmetic functions formed by these well known functions, and reveal (at a certain level) how the values of these functions are co-related.
Prerequisites: Advanced calculus and some complex analysis (residue theorem, analytic continuation, etc).
Density of Gabor systems (Shahaf Nitzan)
The goal of this project is to obtain new and simpler proofs of several known results in time-frequency Analysis, and to extend these results in some new directions. Here is a detailed description of the project.
Prerequisites: introductory level courses in Fourier Analysis and in the theory of Hilbert spaces (including bounded linear operators).
Graduate students: Michelle Cordier, Mike Doyle, Matt Alexander.